Question

Calculate the values for the 5-number summary of the skewed dataset 11, 12, 12, 13, 13, 13, 14, 14, 15, 19, 25.
The minimum value=
Quartile 1=
The median=
Quartile 3=
The maximum value=

Answer 1

To calculate the 5-number summary of the dataset \(11, 12, 12, 13, 13, 13, 14, 14, 15, 19, 25\), we follow these steps:

1. **Minimum Value**: This is the smallest number in the dataset.
- Minimum = \(11\)

2. **Maximum Value**: This is the largest number in the dataset.
- Maximum = \(25\)

3. **Median**: This is the middle value of the dataset. Since there are 11 values, the median is the 6th value when sorted.
- Median = \(13\) (the 6th value)

4. **Quartile 1 (Q1)**: This is the median of the first half of the dataset (the first 5 values: \(11, 12, 12, 13, 13\)).
- Q1 = Median of \(11, 12, 12, 13, 13\) which is \(12\) (the 3rd value)

5. **Quartile 3 (Q3)**: This is the median of the second half of the dataset (the last 5 values: \(14, 14, 15, 19, 25\)).
- Q3 = Median of \(14, 14, 15, 19, 25\) which is \(15\) (the 3rd value)

Putting it all together, the 5-number summary is:
- Minimum value = \(11\)
- Quartile 1 = \(12\)
- Median = \(13\)
- Quartile 3 = \(15\)
- Maximum value = \(25\)

Thus, the final results are:
- Minimum value = **11**
- Quartile 1 = **12**
- Median = **13**
- Quartile 3 = **15**
- Maximum value = **25**